Invariants
| Base field: | $\F_{23}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 13 x + 87 x^{2} - 299 x^{3} + 529 x^{4}$ |
| Frobenius angles: | $\pm0.207871921947$, $\pm0.310374946937$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.53525.1 |
| Galois group: | $D_{4}$ |
| Jacobians: | $5$ |
| Cyclic group of points: | yes |
This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.
Newton polygon
This isogeny class is ordinary.
| $p$-rank: | $2$ |
| Slopes: | $[0, 0, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $305$ | $283345$ | $151716455$ | $78782660525$ | $41453629822000$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $11$ | $535$ | $12467$ | $281523$ | $6440556$ | $148031155$ | $3404741897$ | $78310681203$ | $1801152333461$ | $41426510927550$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 5 curves (of which all are hyperelliptic):
- $y^2=14 x^6+5 x^5+11 x^4+16 x^2+2 x+2$
- $y^2=19 x^6+12 x^5+2 x^4+14 x^3+5 x^2+8 x+19$
- $y^2=7 x^6+16 x^5+6 x^4+10 x^3+16 x^2+x+13$
- $y^2=5 x^6+16 x^5+18 x^4+4 x^3+21 x^2+3 x+19$
- $y^2=10 x^6+17 x^5+x^4+14 x^3+11 x^2+16 x+22$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{23}$.
Endomorphism algebra over $\F_{23}$| The endomorphism algebra of this simple isogeny class is 4.0.53525.1. |
Base change
This is a primitive isogeny class.
Twists
Below is a list of all twists of this isogeny class.
| Twist | Extension degree | Common base change |
|---|---|---|
| 2.23.n_dj | $2$ | (not in LMFDB) |